Sergey Pshenichnikov

Sign sequences (for example, verbal and musical texts) can be turned into mathematical objects. Words and numbers have become one entity, a representation of a matrix unit, which is a matrix generalization of integers and a hypercomplex number. A matrix unit is a matrix in which one element is equal to unit, and the rest are zeros.

If the words of the text are represented by such matrices, then concatenation (combination while maintaining order) of words and texts becomes an operation of adding matrices.

You can perform transformations with texts using algebraic operations, for example, dividing one text by another with a remainder. Mathematically recognize the sense of text and calculate the context of words. In this case, algebra helps to interpret all the intermediate stages of calculations.

A person sees and hears only what he understands (J.W. Goethe). Understands what he attaches sense to as significant for him. Sense is subjective and depends on the interests, motivations, and feelings of different people.

L. S. Vygotsky distinguished between the concepts of «sense» and «meaning»: «if the «meaning» of a word is an objective reflection of a system of connections and relationships, then « sense» is the introduction of subjective aspects of meaning according to a given moment and situation».

According to G. Frege, «meaning» are properties, relationships of objects, «sense» is only part of these properties. In this case, both “meanings” and «sense» are called one «sign», for example a word. Two people can choose from a list of meanings for one word two non-overlapping fragments (two senses) to interpret it.

Each person, in his personal circumstances, chooses the senses of a sign-word as his part of the list of meanings, which is the cause of misunderstanding. Another person may understand the senses of the same sign as a different part of the list of meanings-properties of this sign-word. The reader and the author can also give different senses to the same words, text as signs.

Theory of comprehension is the knowledge of how to understand another person's spoken and written language close to the sense that person wants to express. This means that the signs are known by which it is possible to recognize that part of the list of meanings that the interlocutor in the given circumstances considers (implies) the sense of the word and text.

Understanding the text in some proximity to the author's idea is a challenge to the intellect and a difficult task of recognizing the sense. Such successful decisions are rare. The work of understanding a text is no less expensive than creating it. Theologian and philosopher Andrei Kuraev likes to repeat that every book has a co-author - a reader.

There are different techniques that allow you to indicate the special sense of words, isolated from the entire variety of meanings. The simplest thing in audio communication is intonation, which controls the importance of fragments of speech or text.

Intonation is a change in the relative pitch of a syllable, a word, and a whole utterance (phrase), for example, specifying the modality of the utterance - to distinguish between a narrative, a question, and an exclamation.

Sound intonation is especially evident in music. A musical text without intonation has no sense at all. The theory of musical intonation was developed by B.V. Asafiev in publications from 1930 to 1947. Asafiev called intonation senseful pronunciation, and defined music as the art of intoned sense.

In writing, sense is controlled by punctuation, references, footnotes, notes, fragmentation, structuring, naming of fragments, and various summaries. These are iconic analogues of intonation.

But the main means of sense marking of the text are repetitions. This is due to the peculiarity of neural processes and structural fixation of real neural networks. To organize new neural connections, repeated excitations of neurons are required, for example during learning.

A simple way is to repeat words in the text. Typically, frequency determines the importance of words in the text (keywords) and the language corpus (frequency dictionaries).

A more advanced form of repetition is contextual repetition, where the sense expressed in different words is repeated. For example, the phrase «or in other words» is often used when trying to convey (repeat) the sense of a statement by resorting to other formulations in another lexicon.

Contextual repetition can be hidden in the text or corpus of language. For example, philosophical categories are latently contained in any fragment of text, but in frequency dictionaries they are at the end of the list and are least often used. The categories «order» and «equivalence» are less common in the language corpus than their hyponyms «more», «less», «more important», «greener»; «equals», «is», «this».

Pronouns (instead of names) are most often used; they are the historical predecessors of philosophical (logical) categories, but these are also higher linguistic hyperonyms.

The language of mathematical and philosophical categories is the future language for describing sense, although it is philosophical words-categories that are called without content (sense). It is always easier to understand the sense of a word through its hypernym. For example, the word «hirola» can be understood through its generic concept «antelope».

The myth about the emptiness of categories is based on the habit of defining a concept through its gender (hyperonym). For rootless concepts (categories) there is then no definition, sense, or content.

But the definition of concepts can optionally be given only on a pair of categories «part» - «whole» («hyponym» - «hyperonym», «species» - «genus»). The best definition of concepts is their ontological definition through other categories.

In this case, the definitional-judgments use heterarchical (network) connections that satisfy the transitivity condition, in contrast to hierarchical relationships («part» - «whole»).

For philosophical categories (as well as for mathematical ones), the condition of transitivity is satisfied. It is possible to build a system of interrelated concepts: if the first concept relates to the second, which relates to the third concept, there is a connection between the first concept and the third.

A complete system of concepts (theory) has such a triangle of transitivity as its element. But, for example, for such seven concepts «a road of the seventh category is when the forest is felled, but not removed», only instructions can be issued instead of a theory.

Philosophical categories are defined only through each other, creating an example of network definitions. Therefore, the definition template is the transitivity triangle. Similarly, for the definition of mathematical concepts in category theory, the main requirement is the transitivity of relations.

Often the «for example» technique is used to convey sense. The sense that needs to be conveyed to the listener or reader is illustrated by descriptions from another subject area by analogy. In this case, abstraction, or specification of the description in comparison with the original one is allowed.

There are three directions in which elements of the future theory of understanding have already been successfully implemented in practice. These are sense translation, decision support and collective reason.

The need for sense translation, even within one language, is due to the polysemy of words in a natural language. The reader or listener, like a translation from a foreign language, can replace some words with others, the sense of which is clear to him and unambiguous for him.

Words are replaced based on a sense hypothesis, which is formed while reading or listening. In this case, the senses of the source text and the translated text must be similar, which requires computational verification.

Sense translation is a retelling of a text read or heard in your own words. A retelling can become an independent work. The author-reteller, like a good translator from a foreign language, is not obliged to make an accurate translation.

The author of the retelling can and is free to change the structure of the original work, the sequence of presentation, for example, start from the end. You can exclude fragments and present them in the style of another writer. And finally, the pinnacle of the skill of retelling is the presentation of the source text in another genre: tragedy instead of comedy, poetry instead of prose, lyrics instead of reportage, anecdote instead of mathematics, and all the above mixed together.

Several thousand short and dull retellings of literary works are posted in the Briefly library (briefly.ru). This may be the initial stage of creating the genre of retelling and the new profession of «reteller».

If all the above is offered to the authors, then the next creative peak is possible - a synthetic retelling of several works of different genres and authors. With obligatory reference to primary sources.

In algebra of text, sense translation is based on the use of two matrices of paired definitions. The elements of the matrices are the general contexts of pairs of words.

The names of the rows and columns of the matrices of paired definitions are two sets of words. One set is a dictionary of text translated according to its sense. The second set is the words of the personal dictionary of the sense translator.

The first square matrix is filled with source text contexts. This is a matrix notation of a simple definition of one word in terms of another. The content of the definition is the sense of the pairwise relationship of words, written in the corresponding element of the matrix of paired definitions.

Line-by-line sums of matrix texts of a matrix of paired definitions form a composite definition of a word relative to the sense of all other words of the source text.

Pairwise division with the remainder of lowercase compound definitions form a heterarchical system of relations between words according to common factors (modules of comparison by analogy with integers) and remainders (residues), which categorize the contexts of words according to differences. Such contextual dictionaries with network connections are called sense ontologies.

Let the personal contextual dictionary of the sense translator also be presented in the form of an ontology. Then sense translation or retelling consists in establishing relationships between the words of the source text and the words of the translator that have a common context with an acceptable measure (module) of sense accuracy.

A collective retelling is possible. This is the primary form of collective reason. The retold work must be presented as holistic in content, style, genre, and contextual vocabulary. The authors of a collective retelling as a separate project are forced to adapt to each other, to coordinate their personal vocabularies, which is an excellent exercise in the mental unity of the author’s community.

In algebra of text, this means coordinating the personal sense ontologies of the participants and compiling a common ontology. The coordination of ontologies of participants occurs according to the same scheme as the coordination of ontologies during sense translation by one participant. Next, you should make a sense translation of the text using the common ontology of the participants as a common contextual dictionary of the community.

It is useful to precede a collective retelling with a collective sense reading.

It is possible to develop the following areas - personal contextual dictionaries and ontologies, category language sense markup of text and speech, sense preparation of meetings, sense navigation, determination of goals and criteria, calculation of compound judgments, comprehension coaching, think together, sense marketplace, sense signaling system.

Algebra of text can be useful in the development of each direction as a method for recognizing sense.

Decision support is the second example of the successful implementation of a certain class of sense recognition tasks. This is the calculation of one complex estimate from many simple estimates.

Estimates constitute a significant part of conscious activity. A person understands how to formulate a value judgment in a simple situation, but he often does not understand and does not know how to then assemble a composite judgment from the simple judgments made. Especially when the criteria for choosing alternatives are themselves of different importance.

The construction of complex value judgments belongs to the class of multicriteria problems, when it is impossible to find a solution that ideally satisfies all unequally important criteria-requirements leading to the goal.

For example, a buyer at a car dealership can determine the requirements for individual properties of his future car but does not understand how to decide to purchase one car out of a dozen presented. Not a single car in a car dealership fully satisfies all requirements. Such an ideal car may not exist on the market at all.

Evaluation is a subjective determination of the sense of the importance of objects and phenomena. Evaluation involves comparing the subjective sense of an object with its concept, which plays the role of a criterion, measure, norm, standard, equivalent.

Composite value judgments are a different kind of property-relations and a different kind of understanding than simply understanding text or speech. To understand the latter and their semantic translation, relations of equality (equivalence) or similarity (tolerance) are required. The object and predicate of the judgment are connected by the connective «this is in the sense».

To make decisions, words in a judgment are connected by the connective «more important in sense». These are relations of order to which value judgments correspond.

The concept of «evaluation» is generic for terms-relations of equality and order, which in turn are generic concepts for many words of natural language - comparative adverbs and adjectives.

The third example of successful recognition of sense is the elements of collective reason manifested in GitHub and Habr.

In all examples of the manifestation of collective i reason, the most important thing is the ability to understand how a new idea (conclusion, retelling) or a composite judgment (decision making) was obtained. This is not always carried out and considered in the technical requirements of the project. For example, artificial intelligence methods simulate the phenomenon of intuition and the human intellect. In this case, it is impossible to understand how the result was obtained. On the contrary, algebraic methods model the human mind. The logic behind obtaining the result can be transparent and understandable, since all the «commits» of the calculations are known.

Intellect is the accidental generality of a part, the ability of thinking to extract a lot from a little. Adaptive feature of individual people unencumbered by mental prejudices. Eggheads are very useful for the collective reason to refute dogmas, axioms, formulations of hypotheses and goals. At the same time, the results of smart ones are unpredictable in terms of time of receipt and their quality. Random. Smart passionaries (according to Gumilyov) are useful and dangerous for the future of a reason collective super ethnos. Intuitive thinking is thinking without rules, a flexible and willful play of thoughts.

The intellect looks for the general in the particular, bases the general on the particular (as in machine learning). A person can have intelligence despite the presence of knowledge and education. The need for intelligence occurs when knowledge and data are lacking. The psychophysical basis of the mind is imagination. According to Descartes, intuition is the intellect of imagination. The instrument of the intellect is intuition. The intellect is the dictate of the particular over the general. Intuition is unique, individual, particular, striving for the general, inspiring and at the same time irritating the mind.

Mind is a necessary part of the whole, the ability of thinking to extract a little from a lot. An example of this type of thinking is that a ~~well-tempered~~, ordered database allows you to quickly, upon request, be guaranteed (necessary) to find an answer. The basis of reason is erudition. The psychophysical basis of mind is memory. According to Descartes, deduction is the intellect of memory. The instrument of activity of the intellect of mind is deductive logic. Mind is general, generic, repeating, necessary, natural. Logical thinking is rigid, ordered, logical (necessary) thinking according to the rules. Mind is the dictate of the general over the particular.

Reason is the specific necessary and random ideal combination of parts of the whole for the universal, the optimal synthesis of intellect and mind. Impossible in one person. The main mistake of modern philosophy is that the possibility of the existence of reason in one head of Homo sapiens is accepted as an implicit assumption.

For optimal synthesis of intellect and mind, you need at least three ~~drinking buddies~~ heads, like the Serpent Gorynych - a symbol of the collective reason.

The assumption of the founding-fathers of classical philosophy about the possibility of the existence of reason in an individual person is incorrect. There is not a single historical example. But the implementation of such an assumption leads in practice to the trust management of communities by hierarchs devoid of reason, which can only be collective.

The entire history of mankind confirms the depravity of the practice of transferring decision-making to the voter in trust. And this is a great merit of the ideological creators of the non-existent individual reason - numerous philosophical schools and their representatives.

Each wisdom school mentor had one of two characteristics. For example (according to L.E. Balashov), rationality (mind) prevailed in the thinking of Spinoza, Leibniz, and Wolf. In Feuerbach, Nietzsche, Berkeley, Hume, Hobbes, Locke, Berdyaev, intelligence prevailed. The classification can be continued. And there will be no one in the class of reason. Even Kant and Hegel will turn out to be only rationalists (mind). One can fantasize about their simulated, model future participation in the collective reason.

Collective philosophy is about how it is optimal for a specific task to metaphysically unite people with different categorical relationships of logos, pathos, and ethos into a collective reason.

The theory of collective reason of the human population does not currently exist, as they now say, «from the word at all». A necessary requirement for creating a collective reason is a theory of understanding and the emergence of a supernova human ability - to think together. Rarely emerging reason human communities with strong motivation are extremely unstable and short-lived groups.

According to Claude Lévi-Strauss (an anthropologist who uses the methods of structural linguistics) «... understanding consists in bringing one kind of reality to another; (because) true reality is never obvious... ».

An overview of the history of the development of the concept of «sense» is available in the works of D.A. Leontyev. Leontiev believes that if we generalize all interpretations of sense in philosophy and the humanities (except for V.V. Nalimov’s approach on probabilistic sense filters), then the sense (of texts, images of consciousness or actions) is determined by context and intention (goal orientation), as two of its defining properties.

LITERATURE

Sergey Pshenichnikov. Algebra of text for judgments. Self-tutorial understanding. Ridero. 2024. 159 p. ISBN 978-5-0062-3246-4

https://ridero.ru/books/algebra_of_text_for_judgments_self-tutorial_understanding/

https://www.researchgate.net/publication/377985752_Algebra_of_text_for_judgments_Self-tutorial_understanding

ALGEBRA OF SENSE